Nonlinear optics optical rotation effects

Optical parametric oscillators (OPOs) represent another tunable soHd-state source, based on nonlinear optical effects. These have been under development for many years and as of this writing (ca 1994) are beginning to become commercially available. These lasers may be tuned by temperature or by rotating a crystal. Models available cover a broad wavelength range in the visible and infrared portions of the spectmm. One commercial device may be tuned from 410 to 2000 nm. 

This effect, which is in a loose sense the nonlinear analog of linear optical rotation, is based on using linearly polarized fundamental light and measuring the direction of the major axis of the ellipse that describes the state of polarization of the second-harmonic light. For a simple description of the effect, we assume that the expansion coefficients are real, as would be the case for nonresonant excitation within the electric dipole approximation.22 In this case, the second-harmonic light will also be linearly polarized in a direction characterized by the angle... 

The Pockel s effect [3] refers to an electro-optical process wherein the application of large electric fields onto crystals lacking a center of symmetry can lead to nonlinear polarization effects and optical rotation. Pockel cells can be used in place of photoelastic modulators and can achieve very high modulation frequencies but often have the undesirable property of a nonzero birefringence in the absence of an applied field. 

The nonlinear optical properties of rotaxanes and catenanes were studied mainly by three techniques the optical second and third harmonic generation and the electro-optic Kerr effect. As already mentioned, the harmonic generation techniques give the fast, electronic in origin, molecular and bulk hyperpolarizabili-ties, whereas the electro-optic methods are sensitive to all effects which induce optical birefringence, such as e.g. the rotation of molecules. Therefore the last technique is very useful to study the rotational mobility of molecules and/or their parts. 

Cooperative effects of the monomer units along the polymer backbone may result in a nonlinear relation between the specific optical rotation and the enantiomeric excess (ee) of chiral units present in the polymer [91]. For stiff helical isocyanates, these cooperative effects have led to observations referred to as majority-rules. The role of cooperative effects in chiral rr-PATs has also been examined using a series of PTs containing various ratios of chiral and achiral side chains. Data show that the cooperative interaction between the side chains affects the optical activity in a nonlinear fashion, while the majority-rules principle is applicable to chiral rr-PATs, the magnitude is less pronounced than with helical main-chain isocyanates [91]. 

A well-known nonlinear process taking place in the liquid state of anisotropic molecules is the optical-field induced birefringence (optical Kerr effect ). This nonlinearity results from the reorientation of the molecules in the electric field of a light beam. In the isotropic phase the optical field perturbs the orientational distribution of the molecules. In the perturbed state more molecules are aligned parallel to the electric field than perpendicularly to it and as a consequence the medium becomes birefringent. On the other hand in liquid crystals the orientational distribution of the molecules is inherently anisotropic. The optical field, just as a d.c. electric or magnetic field, induces a collective rotation of the molecules. This process can be described as a reorientation of the director. 

We also realize that the induced molecular precession requires a deposition of the beam energy in the medium. Since the medium is transparent, this can only happen if part of the beam is downward shifted in frequency. Indeed, the rotation of the polarization ellipse means that the two circularly polarized components of the elliptical polarization have different frequencies (o and (o respectively, with fi) fi) 2ft. Using a heterodyne technique, we were able to measure directly the w component in the output. In this respect, we can also regard the present nonlinear optical effect as a stimulated light-scattering process in which a new frequency component at (o is generated. Details of our experiment and theoretical description will be reported elsewhere. 

We also mention the following interesting effect, which curs, e.g., in planar-homeotropic (hybrid) oriented LC s and is not directly related to nonlinear optical effects, ccording to (10), in the adiabatic approximation with 0, the polarization vector of the light wave transmitted f the cell will be rotated by 90 relative to the incident wave Dlarization. A wave with polarization e = incident in le ZvF plane will be an ordinary wave (o-wave) if it is inci- nt from the homeotropic wall (z = 0) and an e-wave if it is cident from the planar wall (z = ). 

Liquid crystals are generally characterized by the strong correlation between molecules, which respond cooperatively to external perturbations. That strong molecular reorientation (or director reorientation) can be easily induced by a static electric or magnetic field is a well-known phenomenon. The same effect induced by optical fields was, however, only studied recently. " Unusually large nonlinear optical effects based on the optical-field-induced molecular reorientation have been observed in nematic liquid-crystal films under the illumination of one or more cw laser beams. In these cases, both the static and dynamical properties of this field-induced molecular motion are found to obey the Ericksen-Leslie continuum theory, which describe the collective molecular reorientation by the rotation of a director (average molecular orientation). 

The existence or nonexistence of mirror symmetry plays an important role in nature. The lack of mirror symmetry, called chirality, can be found in systems of all length scales, from elementary particles to macroscopic systems. Due to the collective behavior of the molecules in liquid crystals, molecular chirality has a particularly remarkable influence on the macroscopic physical properties of these systems. Probably, even the flrst observations of thermotropic liquid crystals by Planer (1861) and Reinitzer (1888) were due to the conspicuous selective reflection of the helical structure that occurs in chiral liquid crystals. Many physical properties of liquid crystals depend on chirality, e.g., certain linear and nonlinear optical properties, the occurrence of ferro-, ferri-, antiferro- and piezo-electric behavior, the electroclinic effect, and even the appearance of new phases. In addition, the majority of optical applications of liquid crystals is due to chiral structures, namely the ther-mochromic effect of cholesteric liquid crystals, the rotation of the plane of polarization in twisted nematic liquid crystal displays, and the ferroelectric and antiferroelectric switching of smectic liquid crystals. 

Raman spectroscopy comprises a family of spectral measurements based on inelastic optical scattering of photons at molecules or crystals. It involves vibrational measurements as well as rotational or electronic studies and nonlinear effects. Following, Raman will be used in the established but slightly inaccurate way as a synonym for the most important and most common technique of the family, linear vibrational Raman scattering. 

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